Coagulation in aerosol and other particulate or colloidal processes is described typically by the Smoluchowski theory. Corrections to that have been developed for van der Waals forces, charged or non-spherical particles and other particle interactions without altering, however, its basic theoretical framework. By definition, the Smoluchowski equation cannot describe coagulation at high particle concentrations (effective volume fraction above 1%). Such concentrations can be encountered in large scale aerosol manufacture of materials as fumed silica (1) and titania (2) as well as alumina and carbon black or soot.

The present work extends the coagulation theory for concentrated aerosols to the free molecule and transition regimes (3). Subsequently, Langevin dynamics (LD) simulations tracing individual particle trajectories were carried out for polydisperse, spherical aerosols at high concentrations. The influence of the particle concentration on coagulation rate and size distribution is investigated with aerosols growing continuously from the free molecule through transition into the continuum regime where coagulation rates are 2 - 30 times higher than that of classic Smoluchowski theory. A relationship is developed for the aerosol coagulation rate of highly concentrated aerosols from the free molecule to continuum regime.

Applications of this theory are in materials synthesis at high temperatures and/or low pressure. The evolution of the enhancement of coagulation rate and the particle size distribution under the influence of particle concentration and size is discussed. Furthermore deviations from ideal behavior in the free molecular regime are presented and discussed.

1. M.C. Heine, S.E. Pratsinis, "High Concentration Agglomerate Dynamics at High Temperatures", Langmuir, 22, 10238-10245 (2006).

2. M.C. Heine, S.E. Pratsinis, "Agglomerate TiO₂ Aerosol Dynamics at High Concentration", Part. Part. Syst. Charact., 24, 56-65 (2007).

3. M.C. Heine, S.E. Pratsinis, "Brownian coagulation at high concentrations", Langmuir, 23, 9882-9890 (2007).